LMFDB - Embedded newform 525.3.s.h.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(124,525)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.124");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 22x^{14} + 343x^{12} - 2542x^{10} + 13621x^{8} - 35080x^{6} + 64300x^{4} - 28000x^{2} + 10000 $ x^16 - 22x^14 + 343x^12 - 2542x^10 + 13621x^8 - 35080x^6 + 64300x^4 - 28000*x^2 + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-2.18275 - 1.26021i$ of defining polynomial
Character	$\chi$	$=$	525.199
Dual form			525.3.s.h.124.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18275 + 1.26021i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.17628 - 2.03737i) q^{4} +4.36551i q^{6} +(3.28656 + 6.18050i) q^{7} -4.15226i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-2.18275 + 1.26021i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.17628 - 2.03737i) q^{4} +4.36551i q^{6} +(3.28656 + 6.18050i) q^{7} -4.15226i q^{8} +(-1.50000 - 2.59808i) q^{9} +(4.36036 - 7.55236i) q^{11} +(-2.03737 - 3.52883i) q^{12} -21.5286 q^{13} +(-14.9625 - 9.34874i) q^{14} +(9.93785 + 17.2129i) q^{16} +(-10.8462 + 18.7862i) q^{17} +(6.54826 + 3.78064i) q^{18} +(2.71590 - 1.56803i) q^{19} +(12.1170 + 0.422628i) q^{21} +21.9799i q^{22} +(3.55799 - 2.05421i) q^{23} +(-6.22840 - 3.59597i) q^{24} +(46.9917 - 27.1307i) q^{26} -5.19615 q^{27} +(16.4579 + 0.574033i) q^{28} +50.8583 q^{29} +(-33.9213 - 19.5845i) q^{31} +(-28.9999 - 16.7431i) q^{32} +(-7.55236 - 13.0811i) q^{33} -54.6743i q^{34} -7.05767 q^{36} +(-45.8831 + 26.4906i) q^{37} +(-3.95209 + 6.84523i) q^{38} +(-18.6443 + 32.2929i) q^{39} +36.8122i q^{41} +(-26.9810 + 14.3475i) q^{42} +17.6504i q^{43} +(-10.2580 - 17.7674i) q^{44} +(-5.17748 + 8.96766i) q^{46} +(2.01959 + 3.49804i) q^{47} +34.4257 q^{48} +(-27.3971 + 40.6251i) q^{49} +(18.7862 + 32.5387i) q^{51} +(-25.3236 + 43.8618i) q^{52} +(-3.85542 - 2.22593i) q^{53} +(11.3419 - 6.54826i) q^{54} +(25.6631 - 13.6467i) q^{56} -5.43180i q^{57} +(-111.011 + 64.0923i) q^{58} +(-81.5032 - 47.0559i) q^{59} +(-63.3781 + 36.5913i) q^{61} +98.7226 q^{62} +(11.1276 - 17.8095i) q^{63} +4.89677 q^{64} +(32.9699 + 19.0352i) q^{66} +(-87.0635 - 50.2661i) q^{67} +(25.5164 + 44.1956i) q^{68} -7.11598i q^{69} -56.6975 q^{71} +(-10.7879 + 6.22840i) q^{72} +(-37.4147 + 64.8042i) q^{73} +(66.7676 - 115.645i) q^{74} -7.37773i q^{76} +(61.0079 + 2.12789i) q^{77} -93.9833i q^{78} +(14.4903 + 25.0980i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-46.3912 - 80.3519i) q^{82} -21.1116 q^{83} +(15.1140 - 24.1897i) q^{84} +(-22.2433 - 38.5266i) q^{86} +(44.0446 - 76.2875i) q^{87} +(-31.3594 - 18.1054i) q^{88} +(-63.1066 + 36.4346i) q^{89} +(-70.7551 - 133.057i) q^{91} -9.66528i q^{92} +(-58.7535 + 33.9213i) q^{93} +(-8.81655 - 5.09024i) q^{94} +(-50.2293 + 28.9999i) q^{96} +73.7985 q^{97} +(8.60469 - 123.201i) q^{98} -26.1622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 12 * q^4 - 24 * q^9	$ 16 q + 12 q^{4} - 24 q^{9} + 40 q^{11} + 32 q^{14} - 4 q^{16} + 96 q^{21} - 96 q^{24} + 240 q^{26} + 200 q^{29} - 252 q^{31} - 72 q^{36} + 24 q^{39} + 36 q^{44} - 164 q^{46} - 76 q^{49} + 36 q^{51} - 36 q^{54} + 392 q^{56} + 108 q^{59} - 792 q^{61} + 8 q^{64} + 48 q^{66} + 328 q^{71} + 280 q^{74} + 412 q^{79} - 72 q^{81} - 264 q^{84} + 356 q^{86} - 564 q^{89} - 228 q^{91} - 60 q^{94} - 216 q^{96} - 240 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 - 24 * q^9 + 40 * q^11 + 32 * q^14 - 4 * q^16 + 96 * q^21 - 96 * q^24 + 240 * q^26 + 200 * q^29 - 252 * q^31 - 72 * q^36 + 24 * q^39 + 36 * q^44 - 164 * q^46 - 76 * q^49 + 36 * q^51 - 36 * q^54 + 392 * q^56 + 108 * q^59 - 792 * q^61 + 8 * q^64 + 48 * q^66 + 328 * q^71 + 280 * q^74 + 412 * q^79 - 72 * q^81 - 264 * q^84 + 356 * q^86 - 564 * q^89 - 228 * q^91 - 60 * q^94 - 216 * q^96 - 240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.18275	+	1.26021i	−1.09138	+	0.630107i	−0.933943	−	0.357423i	$-0.883656\pi$
$2$	−2.18275	+	1.26021i	−1.09138	+	0.630107i	−0.157434	+	0.987529i	$0.550322\pi$
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.17628	−	2.03737i	0.294069	−	0.509343i
$5$		0			0
$5$		0			0
$6$			4.36551i			0.727585i
$7$	3.28656	+	6.18050i	0.469508	+	0.882928i
$7$	3.28656	+	6.18050i	0.469508	+	0.882928i
$8$		−	4.15226i		−	0.519033i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.36036	−	7.55236i	0.396396	−	0.686579i	−0.596882	−	0.802329i	$-0.703594\pi$
$11$	4.36036	−	7.55236i	0.396396	−	0.686579i	0.993278	+	0.115750i	$0.0369273\pi$
$12$	−2.03737	−	3.52883i	−0.169781	−	0.294069i
$13$	−21.5286			−1.65605			−0.828024	−	0.560693i	$-0.810535\pi$
$13$	−21.5286			−1.65605			−0.828024	+	0.560693i	$0.810535\pi$
$14$	−14.9625	−	9.34874i	−1.06875	−	0.667767i
$15$		0			0
$16$	9.93785	+	17.2129i	0.621116	+	1.07580i
$17$	−10.8462	+	18.7862i	−0.638013	+	1.10507i	0.347855	+	0.937548i	$0.386910\pi$
$17$	−10.8462	+	18.7862i	−0.638013	+	1.10507i	−0.985868	+	0.167523i	$0.946423\pi$
$18$	6.54826	+	3.78064i	0.363792	+	0.210036i
$19$	2.71590	−	1.56803i	0.142942	−	0.0825276i	−0.426823	−	0.904335i	$-0.640367\pi$
$19$	2.71590	−	1.56803i	0.142942	−	0.0825276i	0.569765	+	0.821807i	$0.307034\pi$
$20$		0			0
$21$	12.1170	+	0.422628i	0.576999	+	0.0201251i
$22$			21.9799i			0.999088i
$23$	3.55799	−	2.05421i	0.154695	−	0.0893134i	−0.420654	−	0.907221i	$-0.638199\pi$
$23$	3.55799	−	2.05421i	0.154695	−	0.0893134i	0.575349	+	0.817908i	$0.304866\pi$
$24$	−6.22840	−	3.59597i	−0.259517	−	0.149832i
$25$		0			0
$26$	46.9917	−	27.1307i	1.80737	−	1.04349i
$27$	−5.19615			−0.192450
$28$	16.4579	+	0.574033i	0.587781	+	0.0205012i
$29$	50.8583			1.75373			0.876867	−	0.480732i	$-0.159629\pi$
$29$	50.8583			1.75373			0.876867	+	0.480732i	$0.159629\pi$
$30$		0			0
$31$	−33.9213	−	19.5845i	−1.09424	−	0.631758i	−0.159536	−	0.987192i	$-0.551000\pi$
$31$	−33.9213	−	19.5845i	−1.09424	−	0.631758i	−0.934701	+	0.355434i	$0.884333\pi$
$32$	−28.9999	−	16.7431i	−0.906247	−	0.523222i
$33$	−7.55236	−	13.0811i	−0.228860	−	0.396396i
$34$		−	54.6743i		−	1.60807i
$35$		0			0
$36$	−7.05767			−0.196046
$37$	−45.8831	+	26.4906i	−1.24008	+	0.715962i	−0.969111	−	0.246625i	$-0.920678\pi$
$37$	−45.8831	+	26.4906i	−1.24008	+	0.715962i	−0.270972	+	0.962587i	$0.587345\pi$
$38$	−3.95209	+	6.84523i	−0.104002	+	0.180138i
$39$	−18.6443	+	32.2929i	−0.478060	+	0.828024i
$40$		0			0
$41$			36.8122i			0.897857i	0.893568	+	0.448929i	$0.148194\pi$
$41$			36.8122i			0.897857i	−0.893568	+	0.448929i	$0.851806\pi$
$42$	−26.9810	+	14.3475i	−0.642405	+	0.341607i
$43$			17.6504i			0.410475i	0.978712	+	0.205238i	$0.0657967\pi$
$43$			17.6504i			0.410475i	−0.978712	+	0.205238i	$0.934203\pi$
$44$	−10.2580	−	17.7674i	−0.233136	−	0.403804i
$45$		0			0
$46$	−5.17748	+	8.96766i	−0.112554	+	0.194949i
$47$	2.01959	+	3.49804i	0.0429701	+	0.0744263i	0.886711	−	0.462325i	$-0.152985\pi$
$47$	2.01959	+	3.49804i	0.0429701	+	0.0744263i	−0.843740	+	0.536751i	$0.819651\pi$
$48$	34.4257			0.717203
$49$	−27.3971	+	40.6251i	−0.559124	+	0.829084i
$50$		0			0
$51$	18.7862	+	32.5387i	0.368357	+	0.638013i
$52$	−25.3236	+	43.8618i	−0.486993	+	0.843496i
$53$	−3.85542	−	2.22593i	−0.0727438	−	0.0419986i	0.463187	−	0.886261i	$-0.346706\pi$
$53$	−3.85542	−	2.22593i	−0.0727438	−	0.0419986i	−0.535931	+	0.844262i	$0.680039\pi$
$54$	11.3419	−	6.54826i	0.210036	−	0.121264i
$55$		0			0
$56$	25.6631	−	13.6467i	0.458269	−	0.243690i
$57$		−	5.43180i		−	0.0952947i
$58$	−111.011	+	64.0923i	−1.91399	+	1.10504i
$59$	−81.5032	−	47.0559i	−1.38141	−	0.797558i	−0.389084	−	0.921202i	$-0.627208\pi$
$59$	−81.5032	−	47.0559i	−1.38141	−	0.797558i	−0.992327	+	0.123644i	$0.960542\pi$
$60$		0			0
$61$	−63.3781	+	36.5913i	−1.03898	+	0.599858i	−0.919546	−	0.392984i	$-0.871443\pi$
$61$	−63.3781	+	36.5913i	−1.03898	+	0.599858i	−0.119439	+	0.992842i	$0.538110\pi$
$62$	98.7226			1.59230
$63$	11.1276	−	17.8095i	0.176628	−	0.282690i
$64$	4.89677			0.0765121
$65$		0			0
$66$	32.9699	+	19.0352i	0.499544	+	0.288412i
$67$	−87.0635	−	50.2661i	−1.29946	−	0.750241i	−0.319145	−	0.947706i	$-0.603396\pi$
$67$	−87.0635	−	50.2661i	−1.29946	−	0.750241i	−0.980310	+	0.197465i	$0.936729\pi$
$68$	25.5164	+	44.1956i	0.375241	+	0.649936i
$69$		−	7.11598i		−	0.103130i
$70$		0			0
$71$	−56.6975			−0.798557			−0.399278	−	0.916830i	$-0.630739\pi$
$71$	−56.6975			−0.798557			−0.399278	+	0.916830i	$0.630739\pi$
$72$	−10.7879	+	6.22840i	−0.149832	+	0.0865055i
$73$	−37.4147	+	64.8042i	−0.512531	+	0.887729i	0.487364	+	0.873199i	$0.337959\pi$
$73$	−37.4147	+	64.8042i	−0.512531	+	0.887729i	−0.999894	+	0.0145299i	$0.995375\pi$
$74$	66.7676	−	115.645i	0.902266	−	1.56277i
$75$		0			0
$76$		−	7.37773i		−	0.0970754i
$77$	61.0079	+	2.12789i	0.792311	+	0.0276350i
$78$		−	93.9833i		−	1.20491i
$79$	14.4903	+	25.0980i	0.183422	+	0.317696i	0.943044	−	0.332669i	$-0.107949\pi$
$79$	14.4903	+	25.0980i	0.183422	+	0.317696i	−0.759622	+	0.650365i	$0.774616\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−46.3912	−	80.3519i	−0.565746	−	0.979901i
$83$	−21.1116			−0.254357			−0.127179	−	0.991880i	$-0.540592\pi$
$83$	−21.1116			−0.254357			−0.127179	+	0.991880i	$0.540592\pi$
$84$	15.1140	−	24.1897i	0.179928	−	0.287973i
$85$		0			0
$86$	−22.2433	−	38.5266i	−0.258643	−	0.447983i
$87$	44.0446	−	76.2875i	0.506260	−	0.876867i
$88$	−31.3594	−	18.1054i	−0.356357	−	0.205743i
$89$	−63.1066	+	36.4346i	−0.709063	+	0.409378i	−0.810714	−	0.585442i	$-0.800921\pi$
$89$	−63.1066	+	36.4346i	−0.709063	+	0.409378i	0.101651	+	0.994820i	$0.467588\pi$
$90$		0			0
$91$	−70.7551	−	133.057i	−0.777528	−	1.46217i
$92$		−	9.66528i		−	0.105057i
$93$	−58.7535	+	33.9213i	−0.631758	+	0.364746i
$94$	−8.81655	−	5.09024i	−0.0937931	−	0.0541515i
$95$		0			0
$96$	−50.2293	+	28.9999i	−0.523222	+	0.302082i
$97$	73.7985			0.760809			0.380405	−	0.924820i	$-0.375785\pi$
$97$	73.7985			0.760809			0.380405	+	0.924820i	$0.375785\pi$
$98$	8.60469	−	123.201i	0.0878030	−	1.25715i
$99$	−26.1622			−0.264264
$100$		0			0
$101$	−92.6245	−	53.4768i	−0.917075	−	0.529473i	−0.0343741	−	0.999409i	$-0.510944\pi$
$101$	−92.6245	−	53.4768i	−0.917075	−	0.529473i	−0.882701	+	0.469936i	$0.844277\pi$
$102$	−82.0114	−	47.3493i	−0.804033	−	0.464209i
$103$	10.7696	+	18.6535i	0.104559	+	0.181102i	0.913558	−	0.406708i	$-0.133323\pi$
$103$	10.7696	+	18.6535i	0.104559	+	0.181102i	−0.808999	+	0.587810i	$0.799990\pi$
$104$			89.3925i			0.859543i
$105$		0			0
$106$	11.2206			0.105855
$107$	−77.6277	+	44.8184i	−0.725492	+	0.418863i	−0.816771	−	0.576962i	$-0.804238\pi$
$107$	−77.6277	+	44.8184i	−0.725492	+	0.418863i	0.0912785	+	0.995825i	$0.470905\pi$
$108$	−6.11212	+	10.5865i	−0.0565937	+	0.0980232i
$109$	13.6751	−	23.6859i	0.125459	−	0.217302i	−0.796453	−	0.604700i	$-0.793293\pi$
$109$	13.6751	−	23.6859i	0.125459	−	0.217302i	0.921912	+	0.387398i	$0.126626\pi$
$110$		0			0
$111$			91.7661i			0.826722i
$112$	−73.7227	+	117.992i	−0.658238	+	1.05350i
$113$		−	92.3372i		−	0.817144i	−0.912726	−	0.408572i	$-0.866027\pi$
$113$		−	92.3372i		−	0.817144i	0.912726	−	0.408572i	$-0.133973\pi$
$114$	6.84523	+	11.8563i	0.0600459	+	0.104002i
$115$		0			0
$116$	59.8235	−	103.617i	0.515720	−	0.893253i
$117$	32.2929	+	55.9330i	0.276008	+	0.478060i
$118$	237.202			2.01019
$119$	−151.755	−	5.29305i	−1.27525	−	0.0444794i
$120$		0			0
$121$	22.4745	+	38.9270i	0.185740	+	0.321711i
$122$	92.2258	−	159.740i	0.755949	−	1.30934i
$123$	55.2182	+	31.8803i	0.448929	+	0.259189i
$124$	−79.8019	+	46.0736i	−0.643563	+	0.371562i
$125$		0			0
$126$	−1.84498	+	52.8968i	−0.0146427	+	0.419816i
$127$		−	191.591i		−	1.50859i	−0.656534	−	0.754297i	$-0.727978\pi$
$127$		−	191.591i		−	1.50859i	0.656534	−	0.754297i	$-0.272022\pi$
$128$	105.311	−	60.8015i	0.822744	−	0.475011i
$129$	26.4757	+	15.2857i	0.205238	+	0.118494i
$130$		0			0
$131$	50.9329	−	29.4062i	0.388801	−	0.224474i	−0.292839	−	0.956162i	$-0.594600\pi$
$131$	50.9329	−	29.4062i	0.388801	−	0.224474i	0.681641	+	0.731687i	$0.261267\pi$
$132$	−35.5347			−0.269202
$133$	18.6171	+	11.6322i	0.139978	+	0.0874601i
$134$	253.384			1.89093
$135$		0			0
$136$	78.0054	+	45.0364i	0.573569	+	0.331150i
$137$	143.686	+	82.9571i	1.04880	+	0.605526i	0.922314	−	0.386442i	$-0.126296\pi$
$137$	143.686	+	82.9571i	1.04880	+	0.605526i	0.126488	+	0.991968i	$0.459629\pi$
$138$	8.96766	+	15.5324i	0.0649831	+	0.112554i
$139$			139.625i			1.00449i	0.864724	+	0.502247i	$0.167493\pi$
$139$			139.625i			1.00449i	−0.864724	+	0.502247i	$0.832507\pi$
$140$		0			0
$141$	6.99607			0.0496176
$142$	123.757	−	71.4510i	0.871527	−	0.503176i
$143$	−93.8725	+	162.592i	−0.656451	+	1.13701i
$144$	29.8136	−	51.6386i	0.207039	−	0.358601i
$145$		0			0
$146$		−	188.602i		−	1.29180i
$147$	37.2111	+	76.2780i	0.253137	+	0.518898i
$148$			124.641i			0.842171i
$149$	−7.16861	−	12.4164i	−0.0481115	−	0.0833315i	0.840967	−	0.541087i	$-0.181987\pi$
$149$	−7.16861	−	12.4164i	−0.0481115	−	0.0833315i	−0.889078	+	0.457755i	$0.848654\pi$
$150$		0			0
$151$	−106.187	+	183.922i	−0.703226	+	1.21802i	0.264102	+	0.964495i	$0.414925\pi$
$151$	−106.187	+	183.922i	−0.703226	+	1.21802i	−0.967328	+	0.253529i	$0.918409\pi$
$152$	−6.51085	−	11.2771i	−0.0428346	−	0.0741917i
$153$	65.0774			0.425342
$154$	−135.847	+	72.2384i	−0.882123	+	0.469080i
$155$		0			0
$156$	43.8618	+	75.9709i	0.281165	+	0.486993i
$157$	−121.459	+	210.373i	−0.773624	+	1.33996i	0.161941	+	0.986801i	$0.448225\pi$
$157$	−121.459	+	210.373i	−0.773624	+	1.33996i	−0.935565	+	0.353156i	$0.885109\pi$
$158$	−63.2577	−	36.5218i	−0.400365	−	0.231151i
$159$	−6.67778	+	3.85542i	−0.0419986	+	0.0242479i
$160$		0			0
$161$	24.3896	+	15.2389i	0.151488	+	0.0946514i
$162$		−	22.6838i		−	0.140024i
$163$	11.4615	−	6.61728i	0.0703157	−	0.0405968i	−0.464430	−	0.885610i	$-0.653741\pi$
$163$	11.4615	−	6.61728i	0.0703157	−	0.0405968i	0.534746	+	0.845013i	$0.320407\pi$
$164$	75.0001	+	43.3013i	0.457318	+	0.264032i
$165$		0			0
$166$	46.0815	−	26.6052i	0.277600	−	0.160272i
$167$	212.616			1.27315			0.636574	−	0.771216i	$-0.280351\pi$
$167$	212.616			1.27315			0.636574	+	0.771216i	$0.280351\pi$
$168$	1.75486	−	50.3129i	0.0104456	−	0.299482i
$169$	294.481			1.74249
$170$		0			0
$171$	−8.14770	−	4.70408i	−0.0476474	−	0.0275092i
$172$	35.9605	+	20.7618i	0.209073	+	0.120708i
$173$	−124.393	−	215.456i	−0.719037	−	1.24541i	−0.961382	−	0.275219i	$-0.911250\pi$
$173$	−124.393	−	215.456i	−0.719037	−	1.24541i	0.242345	−	0.970190i	$-0.422084\pi$
$174$			222.022i			1.27599i
$175$		0			0
$176$	173.330			0.984832
$177$	−141.168	+	81.5032i	−0.797558	+	0.460470i
$178$	91.8308	−	159.056i	0.515903	−	0.893571i
$179$	27.6352	−	47.8655i	0.154386	−	0.267405i	−0.778449	−	0.627708i	$-0.783993\pi$
$179$	27.6352	−	47.8655i	0.154386	−	0.267405i	0.932835	+	0.360303i	$0.117327\pi$
$180$		0			0
$181$			46.9001i			0.259117i	0.991572	+	0.129558i	$0.0413559\pi$
$181$			46.9001i			0.259117i	−0.991572	+	0.129558i	$0.958644\pi$
$182$	322.122	+	201.265i	1.76990	+	1.10585i
$183$			126.756i			0.692656i
$184$	−8.52961	−	14.7737i	−0.0463566	−	0.0802920i
$185$		0			0
$186$	85.4963	−	148.084i	0.459658	−	0.796150i
$187$	94.5869	+	163.829i	0.505812	+	0.876093i
$188$	9.50241			0.0505447
$189$	−17.0775	−	32.1148i	−0.0903569	−	0.169920i
$190$		0			0
$191$	10.0561	+	17.4177i	0.0526499	+	0.0911923i	0.891149	−	0.453710i	$-0.149900\pi$
$191$	10.0561	+	17.4177i	0.0526499	+	0.0911923i	−0.838499	+	0.544903i	$0.816567\pi$
$192$	4.24073	−	7.34516i	0.0220871	−	0.0382560i
$193$	−24.8578	−	14.3516i	−0.128797	−	0.0743609i	0.434217	−	0.900808i	$-0.357025\pi$
$193$	−24.8578	−	14.3516i	−0.128797	−	0.0743609i	−0.563014	+	0.826447i	$0.690358\pi$
$194$	−161.084	+	93.0019i	−0.830330	+	0.479391i
$195$		0			0
$196$	50.5420	+	103.604i	0.257867	+	0.528594i
$197$		−	224.436i		−	1.13927i	−0.821897	−	0.569636i	$-0.807084\pi$
$197$		−	224.436i		−	1.13927i	0.821897	−	0.569636i	$-0.192916\pi$
$198$	57.1056	−	32.9699i	0.288412	−	0.166515i
$199$	275.447	+	159.030i	1.38416	+	0.799144i	0.992649	−	0.121030i	$-0.0386199\pi$
$199$	275.447	+	159.030i	1.38416	+	0.799144i	0.391509	+	0.920174i	$0.371953\pi$
$200$		0			0
$201$	−150.798	+	87.0635i	−0.750241	+	0.433152i
$202$	269.569			1.33450
$203$	167.149	+	314.330i	0.823393	+	1.54842i
$204$	88.3913			0.433290
$205$		0			0
$206$	−47.0148	−	27.1440i	−0.228227	−	0.131767i
$207$	−10.6740	−	6.16262i	−0.0515651	−	0.0297711i
$208$	−213.948	−	370.569i	−1.02860	−	1.78158i
$209$		−	27.3486i		−	0.130855i
$210$		0			0
$211$	285.317			1.35221			0.676107	−	0.736804i	$-0.263666\pi$
$211$	285.317			1.35221			0.676107	+	0.736804i	$0.263666\pi$
$212$	−9.07009	+	5.23662i	−0.0427835	+	0.0247010i
$213$	−49.1015	+	85.0463i	−0.230523	+	0.399278i
$214$	112.961	−	195.655i	0.527857	−	0.914276i
$215$		0			0
$216$			21.5758i			0.0998880i
$217$	9.55740	−	274.016i	0.0440433	−	1.26275i
$218$			68.9341i			0.316211i
$219$	64.8042	+	112.244i	0.295910	+	0.512531i
$220$		0			0
$221$	233.504	−	404.441i	1.05658	−	1.83005i
$222$	−115.645	−	200.303i	−0.520923	−	0.902266i
$223$	−57.0977			−0.256044			−0.128022	−	0.991771i	$-0.540863\pi$
$223$	−57.0977			−0.256044			−0.128022	+	0.991771i	$0.540863\pi$
$224$	8.17078	−	234.261i	0.0364767	−	1.04581i
$225$		0			0
$226$	116.365	+	201.549i	0.514888	+	0.891812i
$227$	−91.3279	+	158.185i	−0.402325	+	0.696848i	−0.994006	−	0.109324i	$-0.965131\pi$
$227$	−91.3279	+	158.185i	−0.402325	+	0.696848i	0.591681	+	0.806172i	$0.298465\pi$
$228$	−11.0666	−	6.38930i	−0.0485377	−	0.0280233i
$229$	14.5347	−	8.39159i	0.0634702	−	0.0366445i	−0.467929	−	0.883766i	$-0.655000\pi$
$229$	14.5347	−	8.39159i	0.0634702	−	0.0366445i	0.531399	+	0.847121i	$0.321666\pi$
$230$		0			0
$231$	56.0263	−	89.6691i	0.242538	−	0.388178i
$232$		−	211.177i		−	0.910246i
$233$	−230.715	+	133.203i	−0.990193	+	0.571688i	−0.905332	−	0.424704i	$-0.860378\pi$
$233$	−230.715	+	133.203i	−0.990193	+	0.571688i	−0.0848612	+	0.996393i	$0.527045\pi$
$234$	−140.975	−	81.3920i	−0.602457	−	0.347829i
$235$		0			0
$236$	−191.741	+	110.702i	−0.812461	+	0.469075i
$237$	50.1960			0.211797
$238$	337.914	−	179.690i	1.41981	−	0.755001i
$239$	39.7012			0.166114			0.0830568	−	0.996545i	$-0.473532\pi$
$239$	39.7012			0.166114			0.0830568	+	0.996545i	$0.473532\pi$
$240$		0			0
$241$	72.1896	+	41.6787i	0.299542	+	0.172941i	0.642237	−	0.766506i	$-0.278006\pi$
$241$	72.1896	+	41.6787i	0.299542	+	0.172941i	−0.342695	+	0.939447i	$0.611340\pi$
$242$	−98.1128	−	56.6454i	−0.405425	−	0.234072i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			172.166i			0.705600i
$245$		0			0
$246$	−160.704			−0.653267
$247$	−58.4695	+	33.7574i	−0.236719	+	0.136670i
$248$	−81.3200	+	140.850i	−0.327903	+	0.567945i
$249$	−18.2832	+	31.6675i	−0.0734266	+	0.127179i
$250$		0			0
$251$		−	111.464i		−	0.444079i	−0.975038	−	0.222039i	$-0.928729\pi$
$251$		−	111.464i		−	0.444079i	0.975038	−	0.222039i	$-0.0712713\pi$
$252$	−23.1954	−	43.6199i	−0.0920454	−	0.173095i
$253$		−	35.8283i		−	0.141614i
$254$	241.446	+	418.197i	0.950575	+	1.64644i
$255$		0			0
$256$	−163.039	+	282.392i	−0.636872	+	1.10309i
$257$	111.454	+	193.043i	0.433672	+	0.751141i	0.997186	−	0.0749649i	$-0.0238845\pi$
$257$	111.454	+	193.043i	0.433672	+	0.751141i	−0.563515	+	0.826106i	$0.690551\pi$
$258$	−77.0531			−0.298656
$259$	−314.522	−	196.517i	−1.21437	−	0.758754i
$260$		0			0
$261$	−76.2875	−	132.134i	−0.292289	−	0.506260i
$262$	−74.1161	+	128.373i	−0.282886	+	0.489973i
$263$	369.360	+	213.250i	1.40441	+	0.810837i	0.994841	−	0.101442i	$-0.0323457\pi$
$263$	369.360	+	213.250i	1.40441	+	0.810837i	0.409569	+	0.912279i	$0.365679\pi$
$264$	−54.3161	+	31.3594i	−0.205743	+	0.118786i
$265$		0			0
$266$	−55.2957	−	1.92865i	−0.207879	−	0.00725058i
$267$			126.213i			0.472709i
$268$	−204.822	+	118.254i	−0.764260	+	0.441246i
$269$	51.5210	+	29.7457i	0.191528	+	0.110579i	0.592698	−	0.805425i	$-0.298063\pi$
$269$	51.5210	+	29.7457i	0.191528	+	0.110579i	−0.401170	+	0.916004i	$0.631396\pi$
$270$		0			0
$271$	−47.1819	+	27.2405i	−0.174103	+	0.100518i	−0.584519	−	0.811380i	$-0.698717\pi$
$271$	−47.1819	+	27.2405i	−0.174103	+	0.100518i	0.410416	+	0.911898i	$0.365383\pi$
$272$	−431.153			−1.58512
$273$	−260.862	−	9.09858i	−0.955538	−	0.0333281i
$274$	−418.175			−1.52618
$275$		0			0
$276$	−14.4979	−	8.37037i	−0.0525287	−	0.0303274i
$277$	−409.092	−	236.189i	−1.47687	−	0.852669i	−0.477207	−	0.878791i	$-0.658351\pi$
$277$	−409.092	−	236.189i	−1.47687	−	0.852669i	−0.999659	+	0.0261222i	$0.991684\pi$
$278$	−175.957	−	304.766i	−0.632939	−	1.09628i
$279$			117.507i			0.421172i
$280$		0			0
$281$	−534.544			−1.90229			−0.951146	−	0.308743i	$-0.900092\pi$
$281$	−534.544			−1.90229			−0.951146	+	0.308743i	$0.900092\pi$
$282$	−15.2707	+	8.81655i	−0.0541515	+	0.0312644i
$283$	223.638	−	387.352i	0.790239	−	1.36873i	−0.135580	−	0.990766i	$-0.543290\pi$
$283$	223.638	−	387.352i	0.790239	−	1.36873i	0.925819	−	0.377967i	$-0.123377\pi$
$284$	−66.6921	+	115.514i	−0.234831	+	0.406740i
$285$		0			0
$286$		−	473.198i		−	1.65454i
$287$	−227.517	+	120.985i	−0.792743	+	0.421552i
$288$			100.459i			0.348815i
$289$	−90.7814	−	157.238i	−0.314122	−	0.544076i
$290$		0			0
$291$	63.9114	−	110.698i	0.219627	−	0.380405i
$292$	88.0202	+	152.456i	0.301439	+	0.522108i
$293$	504.200			1.72082			0.860409	−	0.509604i	$-0.170208\pi$
$293$	504.200			1.72082			0.860409	+	0.509604i	$0.170208\pi$
$294$	−177.349	−	119.602i	−0.603229	−	0.406810i
$295$		0			0
$296$	109.996	+	190.519i	0.371608	+	0.643644i
$297$	−22.6571	+	39.2432i	−0.0762865	+	0.132132i
$298$	31.2946	+	18.0680i	0.105016	+	0.0606308i
$299$	−76.5986	+	44.2242i	−0.256183	+	0.147907i
$300$		0			0
$301$	−109.088	+	58.0092i	−0.362420	+	0.192722i
$302$		−	535.274i		−	1.77243i
$303$	−160.430	+	92.6245i	−0.529473	+	0.305692i
$304$	53.9804	+	31.1656i	0.177567	+	0.102518i
$305$		0			0
$306$	−142.048	+	82.0114i	−0.464209	+	0.268011i
$307$	398.792			1.29900			0.649499	−	0.760363i	$-0.274979\pi$
$307$	398.792			1.29900			0.649499	+	0.760363i	$0.274979\pi$
$308$	76.0976	−	121.793i	0.247070	−	0.395432i
$309$	37.3070			0.120735
$310$		0			0
$311$	−207.085	−	119.561i	−0.665869	−	0.384440i	0.128640	−	0.991691i	$-0.458939\pi$
$311$	−207.085	−	119.561i	−0.665869	−	0.384440i	−0.794510	+	0.607252i	$0.792272\pi$
$312$	134.089	+	77.4162i	0.429772	+	0.248129i
$313$	111.599	+	193.296i	0.356548	+	0.617559i	0.987382	−	0.158359i	$-0.0506204\pi$
$313$	111.599	+	193.296i	0.356548	+	0.617559i	−0.630834	+	0.775918i	$0.717287\pi$
$314$		−	612.257i		−	1.94986i
$315$		0			0
$316$	68.1786			0.215755
$317$	247.695	−	143.007i	0.781373	−	0.451126i	−0.0555434	−	0.998456i	$-0.517689\pi$
$317$	247.695	−	143.007i	0.781373	−	0.451126i	0.836917	+	0.547330i	$0.184356\pi$
$318$	9.71731	−	16.8309i	0.0305576	−	0.0529273i
$319$	221.761	−	384.100i	0.695174	−	1.20408i
$320$		0			0
$321$			155.255i			0.483662i
$322$	−72.4407	−	2.52665i	−0.224971	−	0.00784675i
$323$			68.0286i			0.210615i
$324$	10.5865	+	18.3364i	0.0326744	+	0.0565937i
$325$		0			0
$326$	−16.6784	+	28.8878i	−0.0511607	+	0.0886129i
$327$	−23.6859	−	41.0252i	−0.0724340	−	0.125459i
$328$	152.854			0.466018
$329$	−14.9821	+	23.9786i	−0.0455383	+	0.0728833i
$330$		0			0
$331$	−269.512	−	466.809i	−0.814236	−	1.41030i	−0.909875	−	0.414882i	$-0.863823\pi$
$331$	−269.512	−	466.809i	−0.814236	−	1.41030i	0.0956391	−	0.995416i	$-0.469511\pi$
$332$	−24.8332	+	43.0123i	−0.0747987	+	0.129555i
$333$	137.649	+	79.4718i	0.413361	+	0.238654i
$334$	−464.088	+	267.941i	−1.38948	+	0.802219i
$335$		0			0
$336$	113.142	+	212.768i	0.336733	+	0.633238i
$337$		−	68.2484i		−	0.202518i	−0.994860	−	0.101259i	$-0.967713\pi$
$337$		−	68.2484i		−	0.202518i	0.994860	−	0.101259i	$-0.0322870\pi$
$338$	−642.780	+	371.109i	−1.90172	+	1.09796i
$339$	−138.506	−	79.9664i	−0.408572	−	0.235889i
$340$		0			0
$341$	−295.819	+	170.791i	−0.867503	+	0.500853i
$342$	23.7126			0.0693350
$343$	−341.126	−	35.8105i	−0.994535	−	0.104404i
$344$	73.2893			0.213050
$345$		0			0
$346$	543.041	+	313.525i	1.56948	+	0.906141i
$347$	330.731	+	190.947i	0.953114	+	0.550281i	0.894047	−	0.447973i	$-0.147854\pi$
$347$	330.731	+	190.947i	0.953114	+	0.550281i	0.0590672	+	0.998254i	$0.481187\pi$
$348$	−103.617	−	179.470i	−0.297751	−	0.515720i
$349$		−	301.869i		−	0.864953i	−0.901645	−	0.432477i	$-0.857640\pi$
$349$		−	301.869i		−	0.864953i	0.901645	−	0.432477i	$-0.142360\pi$
$350$		0			0
$351$	111.866			0.318706
$352$	−252.900	+	146.012i	−0.718466	+	0.414807i
$353$	−64.0227	+	110.891i	−0.181367	+	0.314138i	−0.942346	−	0.334639i	$-0.891386\pi$
$353$	−64.0227	+	110.891i	−0.181367	+	0.314138i	0.760979	+	0.648776i	$0.224719\pi$
$354$	205.423	−	355.803i	0.580291	−	1.00509i
$355$		0			0
$356$			171.429i			0.481542i
$357$	−139.363	+	223.048i	−0.390373	+	0.624786i
$358$			139.305i			0.389120i
$359$	−262.113	−	453.993i	−0.730119	−	1.26460i	−0.956832	−	0.290642i	$-0.906131\pi$
$359$	−262.113	−	453.993i	−0.730119	−	1.26460i	0.226713	−	0.973962i	$-0.427202\pi$
$360$		0			0
$361$	−175.583	+	304.118i	−0.486378	+	0.842432i
$362$	−59.1041	−	102.371i	−0.163271	−	0.282794i
$363$	77.8541			0.214474
$364$	−354.315	−	12.3581i	−0.973394	−	0.0339509i
$365$		0			0
$366$	−159.740	−	276.677i	−0.436448	−	0.755949i
$367$	17.7941	−	30.8202i	0.0484852	−	0.0839789i	−0.840764	−	0.541401i	$-0.817894\pi$
$367$	17.7941	−	30.8202i	0.0484852	−	0.0839789i	0.889249	+	0.457423i	$0.151227\pi$
$368$	70.7176	+	40.8288i	0.192167	+	0.110948i
$369$	95.6408	−	55.2182i	0.259189	−	0.149643i
$370$		0			0
$371$	1.08627	−	31.1441i	0.00292796	−	0.0839462i
$372$			159.604i			0.429042i
$373$	−231.308	+	133.546i	−0.620128	+	0.358031i	−0.776919	−	0.629601i	$-0.783219\pi$
$373$	−231.308	+	133.546i	−0.620128	+	0.358031i	0.156791	+	0.987632i	$0.449885\pi$
$374$	−412.920	−	238.399i	−1.10406	−	0.637432i
$375$		0			0
$376$	14.5248	−	8.38588i	0.0386297	−	0.0223029i
$377$	−1094.91			−2.90427
$378$	77.7474	+	48.5775i	0.205681	+	0.128512i
$379$	125.687			0.331627			0.165813	−	0.986157i	$-0.446975\pi$
$379$	125.687			0.331627			0.165813	+	0.986157i	$0.446975\pi$
$380$		0			0
$381$	−287.387	−	165.923i	−0.754297	−	0.435493i
$382$	−43.9001	−	25.3457i	−0.114922	−	0.0663501i
$383$	−178.260	−	308.755i	−0.465430	−	0.806149i	0.533790	−	0.845617i	$-0.320767\pi$
$383$	−178.260	−	308.755i	−0.465430	−	0.806149i	−0.999221	+	0.0394677i	$0.987434\pi$
$384$		−	210.622i		−	0.548496i
$385$		0			0
$386$	72.3446			0.187421
$387$	45.8572	−	26.4757i	0.118494	−	0.0684126i
$388$	86.8076	−	150.355i	0.223731	−	0.387513i
$389$	223.316	−	386.795i	0.574078	−	0.994332i	−0.422064	−	0.906566i	$-0.638694\pi$
$389$	223.316	−	386.795i	0.574078	−	0.994332i	0.996141	−	0.0877654i	$-0.0279726\pi$
$390$		0			0
$391$			89.1216i			0.227933i
$392$	168.686	+	113.760i	0.430322	+	0.290204i
$393$		−	101.866i		−	0.259201i
$394$	282.838	+	489.890i	0.717863	+	1.24337i
$395$		0			0
$396$	−30.7740	+	53.3021i	−0.0777120	+	0.134601i
$397$	−303.160	−	525.089i	−0.763627	−	1.32264i	−0.940969	−	0.338492i	$-0.890083\pi$
$397$	−303.160	−	525.089i	−0.763627	−	1.32264i	0.177342	−	0.984149i	$-0.443250\pi$
$398$	−801.645			−2.01418
$399$	33.5712	−	17.8519i	0.0841384	−	0.0447417i
$400$		0			0
$401$	364.402	+	631.163i	0.908734	+	1.57397i	0.815826	+	0.578298i	$0.196283\pi$
$401$	364.402	+	631.163i	0.908734	+	1.57397i	0.0929080	+	0.995675i	$0.470384\pi$
$402$	219.437	−	380.076i	0.545864	−	0.945464i
$403$	730.280	+	421.627i	1.81211	+	1.04622i
$404$	−217.904	+	125.807i	−0.539367	+	0.311404i
$405$		0			0
$406$	−760.967	−	475.461i	−1.87430	−	1.17109i
$407$			462.034i			1.13522i
$408$	135.109	−	78.0054i	0.331150	−	0.191190i
$409$	459.563	+	265.329i	1.12363	+	0.648725i	0.942324	−	0.334702i	$-0.108636\pi$
$409$	459.563	+	265.329i	1.12363	+	0.648725i	0.181301	+	0.983428i	$0.441969\pi$
$410$		0			0
$411$	248.871	−	143.686i	0.605526	−	0.349601i
$412$	50.6722			0.122991
$413$	22.9637	−	658.382i	0.0556021	−	1.59415i
$414$	31.0649			0.0750360
$415$		0			0
$416$	624.328	+	360.456i	1.50079	+	0.866481i
$417$	209.437	+	120.919i	0.502247	+	0.289973i
$418$	34.4651	+	59.6953i	0.0824524	+	0.142812i
$419$			282.637i			0.674552i	0.941406	+	0.337276i	$0.109506\pi$
$419$			282.637i			0.674552i	−0.941406	+	0.337276i	$0.890494\pi$
$420$		0			0
$421$	440.590			1.04653			0.523267	−	0.852169i	$-0.324713\pi$
$421$	440.590			1.04653			0.523267	+	0.852169i	$0.324713\pi$
$422$	−622.777	+	359.560i	−1.47577	+	0.852039i
$423$	6.05878	−	10.4941i	0.0143234	−	0.0248088i
$424$	−9.24264	+	16.0087i	−0.0217987	+	0.0377564i
$425$		0			0
$426$		−	247.514i		−	0.581018i
$427$	−434.448	−	271.448i	−1.01744	−	0.635710i
$428$			210.875i			0.492700i
$429$	162.592	+	281.617i	0.379002	+	0.656451i
$430$		0			0
$431$	63.7174	−	110.362i	0.147836	−	0.256060i	−0.782591	−	0.622536i	$-0.786103\pi$
$431$	63.7174	−	110.362i	0.147836	−	0.256060i	0.930427	+	0.366476i	$0.119436\pi$
$432$	−51.6386	−	89.4407i	−0.119534	−	0.207039i
$433$	−433.284			−1.00066			−0.500328	−	0.865836i	$-0.666787\pi$
$433$	−433.284			−1.00066			−0.500328	+	0.865836i	$0.666787\pi$
$434$	324.458	+	610.155i	0.747599	+	1.40589i
$435$		0			0
$436$	−32.1714	−	55.7225i	−0.0737876	−	0.127804i
$437$	6.44210	−	11.1580i	0.0147416	−	0.0255333i
$438$	−282.903	−	163.334i	−0.645898	−	0.372909i
$439$	54.7578	−	31.6144i	0.124733	−	0.0720146i	−0.436335	−	0.899784i	$-0.643724\pi$
$439$	54.7578	−	31.6144i	0.124733	−	0.0720146i	0.561068	+	0.827770i	$0.310391\pi$
$440$		0			0
$441$	146.643	+	10.2419i	0.332523	+	0.0232244i
$442$			1177.06i			2.66303i
$443$	379.648	−	219.190i	0.856992	−	0.494785i	−0.00601155	−	0.999982i	$-0.501914\pi$
$443$	379.648	−	219.190i	0.856992	−	0.494785i	0.863004	+	0.505197i	$0.168580\pi$
$444$	186.962	+	107.942i	0.421085	+	0.243114i
$445$		0			0
$446$	124.630	−	71.9553i	0.279440	−	0.161335i
$447$	−24.8328			−0.0555544
$448$	16.0935	+	30.2645i	0.0359231	+	0.0675547i
$449$	−214.986			−0.478810			−0.239405	−	0.970920i	$-0.576952\pi$
$449$	−214.986			−0.478810			−0.239405	+	0.970920i	$0.576952\pi$
$450$		0			0
$451$	278.019	+	160.514i	0.616450	+	0.355907i
$452$	−188.125	−	108.614i	−0.416207	−	0.240297i
$453$	183.922	+	318.561i	0.406008	+	0.703226i
$454$		−	460.371i		−	1.01403i
$455$		0			0
$456$	−22.5543			−0.0494611
$457$	208.885	−	120.600i	0.457078	−	0.263894i	−0.253737	−	0.967273i	$-0.581660\pi$
$457$	208.885	−	120.600i	0.457078	−	0.263894i	0.710815	+	0.703379i	$0.248326\pi$
$458$	−21.1504	+	36.6336i	−0.0461799	+	0.0799860i
$459$	56.3587	−	97.6161i	0.122786	−	0.212671i
$460$		0			0
$461$			343.383i			0.744865i	0.928059	+	0.372432i	$0.121476\pi$
$461$			343.383i			0.744865i	−0.928059	+	0.372432i	$0.878524\pi$
$462$	−9.28933	+	266.331i	−0.0201068	+	0.576473i
$463$			74.7714i			0.161493i	0.996735	+	0.0807467i	$0.0257305\pi$
$463$			74.7714i			0.161493i	−0.996735	+	0.0807467i	$0.974270\pi$
$464$	505.422	+	875.417i	1.08927	+	1.88667i
$465$		0			0
$466$	335.730	−	581.501i	0.720450	−	1.24786i
$467$	178.095	+	308.470i	0.381360	+	0.660535i	0.991257	−	0.131946i	$-0.0421225\pi$
$467$	178.095	+	308.470i	0.381360	+	0.660535i	−0.609897	+	0.792481i	$0.708789\pi$
$468$	151.942			0.324662
$469$	24.5303	−	703.298i	0.0523034	−	1.49957i
$470$		0			0
$471$	210.373	+	364.377i	0.446652	+	0.773624i
$472$	−195.389	+	338.423i	−0.413959	+	0.716998i
$473$	133.303	+	76.9623i	0.281824	+	0.162711i
$474$	−109.565	+	63.2577i	−0.231151	+	0.133455i
$475$		0			0
$476$	−189.290	+	302.955i	−0.397668	+	0.636461i
$477$			13.3556i			0.0279991i
$478$	−86.6579	+	50.0319i	−0.181293	+	0.104669i
$479$	−323.678	−	186.876i	−0.675737	−	0.390137i	0.122510	−	0.992467i	$-0.460906\pi$
$479$	−323.678	−	186.876i	−0.675737	−	0.390137i	−0.798247	+	0.602330i	$0.794239\pi$
$480$		0			0
$481$	987.799	−	570.306i	2.05364	−	1.18567i
$482$	−210.096			−0.435884
$483$	43.9803	−	23.3871i	0.0910565	−	0.0484205i
$484$	105.745			0.218482
$485$		0			0
$486$	−34.0258	−	19.6448i	−0.0700119	−	0.0404214i
$487$	673.389	+	388.781i	1.38273	+	0.798319i	0.992482	−	0.122391i	$-0.0390563\pi$
$487$	673.389	+	388.781i	1.38273	+	0.798319i	0.390247	+	0.920710i	$0.372390\pi$
$488$	151.937	+	263.162i	0.311346	+	0.539267i
$489$		−	22.9229i		−	0.0468772i
$490$		0			0
$491$	458.794			0.934407			0.467203	−	0.884150i	$-0.345262\pi$
$491$	458.794			0.934407			0.467203	+	0.884150i	$0.345262\pi$
$492$	129.904	−	75.0001i	0.264032	−	0.152439i
$493$	−551.621	+	955.435i	−1.11891	+	1.93800i
$494$	85.0831	−	147.368i	0.172233	−	0.298316i
$495$		0			0
$496$		−	778.511i		−	1.56958i
$497$	−186.340	−	350.419i	−0.374929	−	0.705068i
$498$		−	92.1631i		−	0.185066i
$499$	317.772	+	550.396i	0.636817	+	1.10300i	0.986127	+	0.165992i	$0.0530826\pi$
$499$	317.772	+	550.396i	0.636817	+	1.10300i	−0.349310	+	0.937007i	$0.613584\pi$
$500$		0			0
$501$	184.131	−	318.924i	0.367526	−	0.636574i
$502$	140.468	+	243.298i	0.279817	+	0.484657i
$503$	10.6561			0.0211852			0.0105926	−	0.999944i	$-0.496628\pi$
$503$	10.6561			0.0211852			0.0105926	+	0.999944i	$0.496628\pi$
$504$	−73.9496	−	46.2046i	−0.146725	−	0.0916757i
$505$		0			0
$506$	45.1514	+	78.2045i	0.0892319	+	0.154554i
$507$	255.028	−	441.722i	0.503014	−	0.871246i
$508$	−390.343	−	225.365i	−0.768392	−	0.443631i
$509$	−706.084	+	407.658i	−1.38720	+	0.800899i	−0.992999	−	0.118126i	$-0.962311\pi$
$509$	−706.084	+	407.658i	−1.38720	+	0.800899i	−0.394200	+	0.919025i	$0.628978\pi$
$510$		0			0
$511$	−523.488	−	18.2587i	−1.02444	−	0.0357313i
$512$		−	335.445i		−	0.655167i
$513$	−14.1122	+	8.14770i	−0.0275092	+	0.0158825i
$514$	−486.552	−	280.911i	−0.946599	−	0.546519i
$515$		0			0
$516$	62.2855	−	35.9605i	0.120708	−	0.0696909i
$517$	35.2246			0.0681327
$518$	934.179	+	32.5832i	1.80343	+	0.0629019i
$519$	−430.911			−0.830273
$520$		0			0
$521$	−383.930	−	221.662i	−0.736911	−	0.425456i	0.0840344	−	0.996463i	$-0.473219\pi$
$521$	−383.930	−	221.662i	−0.736911	−	0.425456i	−0.820945	+	0.571007i	$0.806553\pi$
$522$	333.034	+	192.277i	0.637995	+	0.368347i
$523$	−317.051	−	549.148i	−0.606216	−	1.05000i	−0.991858	−	0.127348i	$-0.959354\pi$
$523$	−317.051	−	549.148i	−0.606216	−	1.05000i	0.385642	−	0.922648i	$-0.373980\pi$
$524$		−	138.359i		−	0.264044i
$525$		0			0
$526$	−1074.96			−2.04366
$527$	735.837	−	424.836i	1.39628	−	0.806140i
$528$	150.109	−	259.996i	0.284297	−	0.492416i
$529$	−256.060	+	443.510i	−0.484046	+	0.838393i
$530$		0			0
$531$			282.335i			0.531705i
$532$	45.5980	−	24.2474i	0.0857106	−	0.0455777i
$533$		−	792.515i		−	1.48689i
$534$	−159.056	−	275.492i	−0.297857	−	0.515903i
$535$		0			0
$536$	−208.718	+	361.511i	−0.389400	+	0.674460i
$537$	−47.8655	−	82.9055i	−0.0891351	−	0.154386i
$538$	−149.944			−0.278706
$539$	187.355	+	384.053i	0.347597	+	0.712528i
$540$		0			0
$541$	87.5750	+	151.684i	0.161876	+	0.280378i	0.935542	−	0.353217i	$-0.114912\pi$
$541$	87.5750	+	151.684i	0.161876	+	0.280378i	−0.773665	+	0.633594i	$0.781579\pi$
$542$	68.6577	−	118.919i	0.126675	−	0.219407i
$543$	70.3501	+	40.6167i	0.129558	+	0.0748005i
$544$	629.079	−	363.199i	1.15640	−	0.667646i
$545$		0			0
$546$	580.864	−	308.882i	1.06385	−	0.565718i
$547$			773.543i			1.41416i	0.707136	+	0.707078i	$0.249987\pi$
$547$			773.543i			1.41416i	−0.707136	+	0.707078i	$0.750013\pi$
$548$	338.029	−	195.161i	0.616841	−	0.356133i
$549$	190.134	+	109.774i	0.346328	+	0.199953i
$550$		0			0
$551$	138.126	−	79.7471i	0.250682	−	0.144732i
$552$	−29.5474			−0.0535280
$553$	−107.495	+	172.043i	−0.194385	+	0.311109i
$554$	1190.60			2.14909
$555$		0			0
$556$	284.468	+	164.237i	0.511632	+	0.295391i
$557$	−655.173	−	378.264i	−1.17625	−	0.679110i	−0.221108	−	0.975249i	$-0.570967\pi$
$557$	−655.173	−	378.264i	−1.17625	−	0.679110i	−0.955145	+	0.296140i	$0.904301\pi$
$558$	−148.084	−	256.489i	−0.265383	−	0.459658i
$559$		−	379.989i		−	0.679766i
$560$		0			0
$561$	327.659			0.584062
$562$	1166.78	−	673.639i	2.07612	−	1.19865i
$563$	260.492	−	451.185i	0.462685	−	0.801394i	−0.536409	−	0.843958i	$-0.680219\pi$
$563$	260.492	−	451.185i	0.462685	−	0.801394i	0.999094	+	0.0425646i	$0.0135528\pi$
$564$	8.22933	−	14.2536i	0.0145910	−	0.0252724i
$565$		0			0
$566$			1127.32i			1.99174i
$567$	−62.9617	−	2.19604i	−0.111044	−	0.00387308i
$568$			235.423i			0.414477i
$569$	−91.5332	−	158.540i	−0.160867	−	0.278629i	0.774313	−	0.632803i	$-0.218096\pi$
$569$	−91.5332	−	158.540i	−0.160867	−	0.278629i	−0.935180	+	0.354173i	$0.884762\pi$
$570$		0			0
$571$	−498.800	+	863.947i	−0.873555	+	1.51304i	−0.0152618	+	0.999884i	$0.504858\pi$
$571$	−498.800	+	863.947i	−0.873555	+	1.51304i	−0.858294	+	0.513159i	$0.828475\pi$
$572$	220.840	+	382.507i	0.386084	+	0.668718i
$573$	34.8355			0.0607949
$574$	344.147	−	550.802i	0.599560	−	0.959585i
$575$		0			0
$576$	−7.34516	−	12.7222i	−0.0127520	−	0.0220871i
$577$	161.158	−	279.135i	0.279304	−	0.483769i	−0.691908	−	0.721986i	$-0.743230\pi$
$577$	161.158	−	279.135i	0.279304	−	0.483769i	0.971212	+	0.238217i	$0.0765629\pi$
$578$	396.307	+	228.808i	0.685652	+	0.395861i
$579$	−43.0549	+	24.8578i	−0.0743609	+	0.0429323i
$580$		0			0
$581$	−69.3847	−	130.480i	−0.119423	−	0.224579i
$582$			322.168i			0.553553i
$583$	−33.6220	+	19.4117i	−0.0576707	+	0.0332962i
$584$	269.084	+	155.356i	0.460761	+	0.266020i
$585$		0			0
$586$	−1100.54	+	635.400i	−1.87806	+	1.08430i
$587$	−406.391			−0.692318			−0.346159	−	0.938176i	$-0.612514\pi$
$587$	−406.391			−0.692318			−0.346159	+	0.938176i	$0.612514\pi$
$588$	199.177	+	13.9111i	0.338737	+	0.0236583i
$589$	−122.836			−0.208550
$590$		0			0
$591$	−336.655	−	194.368i	−0.569636	−	0.328879i
$592$	−911.958	−	526.519i	−1.54047	−	0.889391i
$593$	192.655	+	333.688i	0.324881	+	0.562711i	0.981488	−	0.191522i	$-0.0613423\pi$
$593$	192.655	+	333.688i	0.324881	+	0.562711i	−0.656607	+	0.754233i	$0.728009\pi$
$594$		−	114.211i		−	0.192275i
$595$		0			0
$596$	−33.7291			−0.0565925
$597$	477.089	−	275.447i	0.799144	−	0.461386i
$598$	111.464	−	193.061i	0.186395	−	0.322845i
$599$	−448.272	+	776.430i	−0.748367	+	1.29621i	0.200238	+	0.979747i	$0.435829\pi$
$599$	−448.272	+	776.430i	−0.748367	+	1.29621i	−0.948605	+	0.316463i	$0.897505\pi$
$600$		0			0
$601$		−	599.296i		−	0.997166i	−0.866842	−	0.498583i	$-0.833854\pi$
$601$		−	599.296i		−	0.997166i	0.866842	−	0.498583i	$-0.166146\pi$
$602$	165.009	−	264.095i	0.274102	−	0.438695i
$603$			301.597i			0.500161i
$604$	249.811	+	432.686i	0.413595	+	0.716367i
$605$		0			0
$606$	233.453	−	404.353i	0.385237	−	0.667250i
$607$	246.485	+	426.925i	0.406071	+	0.703336i	0.994445	−	0.105253i	$-0.0335652\pi$
$607$	246.485	+	426.925i	0.406071	+	0.703336i	−0.588374	+	0.808589i	$0.700232\pi$
$608$	−105.014			−0.172721
$609$	616.249	+	21.4941i	1.01190	+	0.0352941i
$610$		0			0
$611$	−43.4790	−	75.3079i	−0.0711604	−	0.123253i
$612$	76.5491	−	132.587i	0.125080	−	0.216645i
$613$	122.079	+	70.4822i	0.199150	+	0.114979i	0.596259	−	0.802792i	$-0.296653\pi$
$613$	122.079	+	70.4822i	0.199150	+	0.114979i	−0.397109	+	0.917771i	$0.629987\pi$
$614$	−870.465	+	502.563i	−1.41770	+	0.818507i
$615$		0			0
$616$	8.83557	−	253.321i	0.0143435	−	0.411236i
$617$		−	61.9853i		−	0.100462i	−0.998738	−	0.0502312i	$-0.984004\pi$
$617$		−	61.9853i		−	0.100462i	0.998738	−	0.0502312i	$-0.0159958\pi$
$618$	−81.4321	+	47.0148i	−0.131767	+	0.0760758i
$619$	549.456	+	317.228i	0.887651	+	0.512485i	0.873173	−	0.487410i	$-0.162058\pi$
$619$	549.456	+	317.228i	0.887651	+	0.512485i	0.0144774	+	0.999895i	$0.495392\pi$
$620$		0			0
$621$	−18.4879	+	10.6740i	−0.0297711	+	0.0171884i
$622$	602.689			0.968953
$623$	−432.588	−	270.286i	−0.694362	−	0.433845i
$624$	−741.138			−1.18772
$625$		0			0
$626$	−487.188	−	281.278i	−0.778256	−	0.449326i
$627$	−41.0229	−	23.6846i	−0.0654273	−	0.0377745i
$628$	285.739	+	494.914i	0.454998	+	0.788080i
$629$		−	1149.29i		−	1.82717i
$630$		0			0
$631$	93.3216			0.147895			0.0739474	−	0.997262i	$-0.476440\pi$
$631$	93.3216			0.147895			0.0739474	+	0.997262i	$0.476440\pi$
$632$	104.213	−	60.1677i	0.164895	−	0.0952020i
$633$	247.092	−	427.976i	0.390350	−	0.676107i
$634$	−360.439	+	624.298i	−0.568515	+	0.984698i
$635$		0			0
$636$			18.1402i			0.0285223i
$637$	589.821	−	874.603i	0.925935	−	1.37300i
$638$			1117.86i			1.75214i
$639$	85.0463	+	147.305i	0.133093	+	0.230523i
$640$		0			0
$641$	−153.961	+	266.668i	−0.240188	+	0.416018i	−0.960768	−	0.277354i	$-0.910543\pi$
$641$	−153.961	+	266.668i	−0.240188	+	0.416018i	0.720579	+	0.693372i	$0.243876\pi$
$642$	−195.655	−	338.884i	−0.304759	−	0.527857i
$643$	−296.519			−0.461150			−0.230575	−	0.973055i	$-0.574061\pi$
$643$	−296.519			−0.461150			−0.230575	+	0.973055i	$0.574061\pi$
$644$	59.7362	−	31.7655i	0.0927581	−	0.0493253i
$645$		0			0
$646$	−85.7306	−	148.490i	−0.132710	−	0.229860i
$647$	117.622	−	203.727i	0.181796	−	0.314880i	−0.760696	−	0.649108i	$-0.775142\pi$
$647$	117.622	−	203.727i	0.181796	−	0.314880i	0.942492	+	0.334228i	$0.108476\pi$
$648$	32.3637	+	18.6852i	0.0499440	+	0.0288352i
$649$	−710.767	+	410.361i	−1.09517	+	0.632298i
$650$		0			0
$651$	−402.748	−	251.641i	−0.618660	−	0.386546i
$652$		−	31.1350i		−	0.0477531i
$653$	257.769	−	148.823i	0.394746	−	0.227906i	−0.289469	−	0.957187i	$-0.593479\pi$
$653$	257.769	−	148.823i	0.394746	−	0.227906i	0.684214	+	0.729281i	$0.260145\pi$
$654$	103.401	+	59.6987i	0.158106	+	0.0912823i
$655$		0			0
$656$	−633.643	+	365.834i	−0.965919	+	0.557673i
$657$	224.488			0.341687
$658$	2.48408	−	71.2200i	0.00377519	−	0.108237i
$659$	127.740			0.193839			0.0969197	−	0.995292i	$-0.469101\pi$
$659$	127.740			0.193839			0.0969197	+	0.995292i	$0.469101\pi$
$660$		0			0
$661$	−823.610	−	475.512i	−1.24601	−	0.719382i	−0.275696	−	0.961245i	$-0.588908\pi$
$661$	−823.610	−	475.512i	−1.24601	−	0.719382i	−0.970311	+	0.241863i	$0.922242\pi$
$662$	1176.56	+	679.286i	1.77728	+	1.02611i
$663$	−404.441	−	700.513i	−0.610017	−	1.05658i
$664$			87.6611i			0.132020i
$665$		0			0
$666$	−400.606			−0.601510
$667$	180.953	−	104.474i	0.271295	−	0.156632i
$668$	250.095	−	433.178i	0.374394	−	0.648469i
$669$	−49.4481	+	85.6466i	−0.0739134	+	0.128022i
$670$		0			0
$671$			638.206i			0.951126i
$672$	−344.316	−	215.132i	−0.512374	−	0.320137i
$673$		−	1003.39i		−	1.49092i	−0.666550	−	0.745460i	$-0.732230\pi$
$673$		−	1003.39i		−	1.49092i	0.666550	−	0.745460i	$-0.267770\pi$
$674$	86.0076	+	148.970i	0.127608	+	0.221023i
$675$		0			0
$676$	346.392	−	599.968i	0.512414	−	0.887526i
$677$	−235.907	−	408.603i	−0.348460	−	0.603550i	0.637516	−	0.770437i	$-0.279962\pi$
$677$	−235.907	−	408.603i	−0.348460	−	0.603550i	−0.985976	+	0.166887i	$0.946629\pi$
$678$	403.099			0.594541
$679$	242.543	+	456.111i	0.357206	+	0.671740i
$680$		0			0
$681$	158.185	+	273.984i	0.232283	+	0.402325i
$682$	430.466	−	745.589i	0.631182	−	1.09324i
$683$	−361.330	−	208.614i	−0.529034	−	0.305438i	0.211589	−	0.977359i	$-0.432136\pi$
$683$	−361.330	−	208.614i	−0.529034	−	0.305438i	−0.740623	+	0.671921i	$0.765470\pi$
$684$	−19.1679	+	11.0666i	−0.0280233	+	0.0161792i
$685$		0			0
$686$	789.722	−	351.726i	1.15120	−	0.512719i
$687$		−	29.0693i		−	0.0423134i
$688$	−303.815	+	175.407i	−0.441591	+	0.254953i
$689$	83.0019	+	47.9211i	0.120467	+	0.0695517i
$690$		0			0
$691$	160.907	−	92.8995i	0.232860	−	0.134442i	−0.379030	−	0.925384i	$-0.623742\pi$
$691$	160.907	−	92.8995i	0.232860	−	0.134442i	0.611891	+	0.790942i	$0.290409\pi$
$692$	−585.285			−0.845787
$693$	−85.9835	−	161.695i	−0.124074	−	0.233326i
$694$	−962.538			−1.38694
$695$		0			0
$696$	−316.766	−	182.885i	−0.455123	−	0.262765i
$697$	−691.561	−	399.273i	−0.992197	−	0.572845i
$698$	380.419	+	658.905i	0.545013	+	0.943990i
$699$			461.430i			0.660129i
$700$		0			0
$701$	1034.80			1.47618			0.738089	−	0.674704i	$-0.235729\pi$
$701$	1034.80			1.47618			0.738089	+	0.674704i	$0.235729\pi$
$702$	−244.176	+	140.975i	−0.347829	+	0.200819i
$703$	−83.0759	+	143.892i	−0.118173	+	0.204682i
$704$	21.3517	−	36.9822i	0.0303291	−	0.0525316i
$705$		0			0
$706$		−	322.729i		−	0.457123i
$707$	26.0971	−	748.220i	0.0369125	−	1.05830i
$708$			383.482i			0.541641i
$709$	−108.321	−	187.618i	−0.152780	−	0.264623i	0.779468	−	0.626442i	$-0.215489\pi$
$709$	−108.321	−	187.618i	−0.152780	−	0.264623i	−0.932248	+	0.361819i	$0.882156\pi$
$710$		0			0
$711$	43.4710	−	75.2940i	0.0611406	−	0.105899i
$712$	151.286	+	262.035i	0.212481	+	0.368027i
$713$	−160.923			−0.225698
$714$	23.1069	−	662.487i	0.0323625	−	0.927854i
$715$		0			0
$716$	−65.0133	−	112.606i	−0.0908007	−	0.157271i
$717$	34.3822	−	59.5517i	0.0479529	−	0.0830568i
$718$	1144.26	+	660.636i	1.59367	+	0.920106i
$719$	−0.325449	+	0.187898i	−0.000452641	+	0.000261332i	−0.500226	−	0.865895i	$-0.666750\pi$
$719$	−0.325449	+	0.187898i	−0.000452641	+	0.000261332i	0.499774	+	0.866156i	$0.333417\pi$
$720$		0			0
$721$	−79.8930	+	127.867i	−0.110809	+	0.177347i
$722$		−	885.086i		−	1.22588i
$723$	125.036	−	72.1896i	0.172941	−	0.0998473i
$724$	95.5530	+	55.1675i	0.131979	+	0.0761983i
$725$		0			0
$726$	−169.936	+	98.1128i	−0.234072	+	0.135142i
$727$	−174.857			−0.240518			−0.120259	−	0.992743i	$-0.538373\pi$
$727$	−174.857			−0.240518			−0.120259	+	0.992743i	$0.538373\pi$
$728$	−552.490	+	293.794i	−0.758915	+	0.403563i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−331.585	−	191.441i	−0.453605	−	0.261889i
$732$	258.249	+	149.100i	0.352800	+	0.203689i
$733$	−426.206	−	738.210i	−0.581454	−	1.00711i	−0.995307	−	0.0967645i	$-0.969151\pi$
$733$	−426.206	−	738.210i	−0.581454	−	1.00711i	0.413853	−	0.910344i	$-0.364183\pi$
$734$			89.6973i			0.122203i
$735$		0			0
$736$	−137.575			−0.186923
$737$	−759.256	+	438.357i	−1.03020	+	0.594785i
$738$	−139.174	+	241.056i	−0.188582	+	0.326634i
$739$	−584.126	+	1011.74i	−0.790428	+	1.36906i	0.135275	+	0.990808i	$0.456808\pi$
$739$	−584.126	+	1011.74i	−0.790428	+	1.36906i	−0.925702	+	0.378253i	$0.876525\pi$
$740$		0			0
$741$			116.939i			0.157813i
$742$	36.8771	+	69.3488i	0.0496996	+	0.0934619i
$743$		−	558.877i		−	0.752190i	−0.926581	−	0.376095i	$-0.877267\pi$
$743$		−	558.877i		−	0.752190i	0.926581	−	0.376095i	$-0.122733\pi$
$744$	140.850	+	243.960i	0.189315	+	0.327903i
$745$		0			0
$746$	336.592	−	582.995i	0.451196	−	0.781494i
$747$	31.6675	+	54.8497i	0.0423929	+	0.0734266i
$748$	445.042			0.594976
$749$	−532.128	−	332.479i	−0.710451	−	0.443898i
$750$		0			0
$751$	−630.654	−	1092.32i	−0.839752	−	1.45449i	−0.890102	−	0.455762i	$-0.849367\pi$
$751$	−630.654	−	1092.32i	−0.839752	−	1.45449i	0.0503493	−	0.998732i	$-0.483967\pi$
$752$	−40.1408	+	69.5260i	−0.0533788	+	0.0924547i
$753$	−167.196	−	96.5304i	−0.222039	−	0.128194i
$754$	2389.92	−	1379.82i	3.16965	−	1.83000i
$755$		0			0
$756$	−85.5177	−	2.98276i	−0.113119	−	0.00394546i
$757$			1269.13i			1.67652i	0.545268	+	0.838262i	$0.316428\pi$
$757$			1269.13i			1.67652i	−0.545268	+	0.838262i	$0.683572\pi$
$758$	−274.343	+	158.392i	−0.361930	+	0.208960i
$759$	−53.7425	−	31.0282i	−0.0708070	−	0.0408804i
$760$		0			0
$761$	−157.718	+	91.0585i	−0.207251	+	0.119656i	−0.600033	−	0.799975i	$-0.704846\pi$
$761$	−157.718	+	91.0585i	−0.207251	+	0.119656i	0.392782	+	0.919632i	$0.371513\pi$
$762$	836.394			1.09763
$763$	191.335	+	6.67355i	0.250766	+	0.00874646i
$764$	47.3152			0.0619309
$765$		0			0
$766$	778.195	+	449.291i	1.01592	+	0.586542i
$767$	1754.65	+	1013.05i	2.28768	+	1.32079i
$768$	282.392	+	489.118i	0.367698	+	0.636872i
$769$			810.237i			1.05362i	0.849982	+	0.526812i	$0.176613\pi$
$769$			810.237i			1.05362i	−0.849982	+	0.526812i	$0.823387\pi$
$770$		0			0
$771$	386.087			0.500761
$772$	−58.4793	+	33.7630i	−0.0757504	+	0.0437345i
$773$	−122.682	+	212.492i	−0.158709	+	0.274893i	−0.934404	−	0.356216i	$-0.884067\pi$
$773$	−122.682	+	212.492i	−0.158709	+	0.274893i	0.775694	+	0.631109i	$0.217400\pi$
$774$	−66.7300	+	115.580i	−0.0862144	+	0.149328i
$775$		0			0
$776$		−	306.431i		−	0.394885i
$777$	−567.160	+	301.595i	−0.729936	+	0.388153i
$778$			1125.70i			1.44692i
$779$	57.7224	+	99.9781i	0.0740981	+	0.128342i
$780$		0			0
$781$	−247.222	+	428.200i	−0.316545	+	0.548272i
$782$	−112.312	−	194.531i	−0.143622	−	0.248760i
$783$	−264.268			−0.337506
$784$	−971.543	−	67.8553i	−1.23921	−	0.0865501i
$785$		0			0
$786$	128.373	+	222.348i	0.163324	+	0.282886i
$787$	−215.363	+	373.020i	−0.273651	+	0.473977i	−0.969794	−	0.243926i	$-0.921565\pi$
$787$	−215.363	+	373.020i	−0.273651	+	0.473977i	0.696143	+	0.717903i	$0.254898\pi$
$788$	−457.261	−	264.000i	−0.580280	−	0.335025i
$789$	639.750	−	369.360i	0.810837	−	0.468137i
$790$		0			0
$791$	570.690	−	303.472i	0.721479	−	0.383656i
$792$			108.632i			0.137162i
$793$	1364.44	−	787.761i	1.72061	−	0.993393i
$794$	1323.45	+	764.093i	1.66681	+	0.962334i
$795$		0			0
$796$	648.005	−	374.126i	0.814077	−	0.470008i
$797$	−1137.61			−1.42737			−0.713684	−	0.700468i	$-0.752975\pi$
$797$	−1137.61			−1.42737			−0.713684	+	0.700468i	$0.752975\pi$
$798$	−50.7805	+	81.2733i	−0.0636347	+	0.101846i
$799$	−87.6199			−0.109662
$800$		0			0
$801$	189.320	+	109.304i	0.236354	+	0.136459i
$802$	−1590.80	−	918.449i	−1.98354	−	1.14520i
$803$	326.283	+	565.139i	0.406330	+	0.703785i
$804$			409.643i			0.509507i
$805$		0			0
$806$	−2125.36			−2.63692
$807$	89.2370	−	51.5210i	0.110579	−	0.0638426i
$808$	−222.050	+	384.602i	−0.274814	+	0.475992i
$809$	455.336	−	788.665i	0.562838	−	0.974864i	−0.434409	−	0.900716i	$-0.643043\pi$
$809$	455.336	−	788.665i	0.562838	−	0.974864i	0.997247	−	0.0741482i	$-0.0236238\pi$
$810$		0			0
$811$			546.361i			0.673688i	0.941560	+	0.336844i	$0.109360\pi$
$811$			546.361i			0.673688i	−0.941560	+	0.336844i	$0.890640\pi$
$812$	837.020	+	29.1944i	1.03081	+	0.0359537i
$813$			94.3638i			0.116069i
$814$	−582.262	−	1008.51i	−0.715309	−	1.23895i
$815$		0			0
$816$	−373.389	+	646.729i	−0.457585	+	0.792560i
$817$	27.6763	+	47.9368i	0.0338756	+	0.0586742i
$818$	−1337.48			−1.63507
$819$	−239.561	+	383.413i	−0.292504	+	0.468148i
$820$		0			0
$821$	−322.150	−	557.980i	−0.392388	−	0.679635i	0.600376	−	0.799718i	$-0.295017\pi$
$821$	−322.150	−	557.980i	−0.392388	−	0.679635i	−0.992764	+	0.120082i	$0.961684\pi$
$822$	−362.150	+	627.262i	−0.440572	+	0.763092i
$823$	−666.252	−	384.661i	−0.809540	−	0.467388i	0.0372559	−	0.999306i	$-0.488138\pi$
$823$	−666.252	−	384.661i	−0.809540	−	0.467388i	−0.846796	+	0.531917i	$0.821472\pi$
$824$	77.4543	−	44.7183i	0.0939980	−	0.0542697i
$825$		0			0
$826$	779.579	+	1466.03i	0.943800	+	1.77485i
$827$		−	715.404i		−	0.865060i	−0.901620	−	0.432530i	$-0.857621\pi$
$827$		−	715.404i		−	0.865060i	0.901620	−	0.432530i	$-0.142379\pi$
$828$	−25.1111	+	14.4979i	−0.0303274	+	0.0175096i
$829$	−68.2973	−	39.4315i	−0.0823852	−	0.0475651i	0.458241	−	0.888828i	$-0.348479\pi$
$829$	−68.2973	−	39.4315i	−0.0823852	−	0.0475651i	−0.540627	+	0.841263i	$0.681813\pi$
$830$		0			0
$831$	−708.568	+	409.092i	−0.852669	+	0.492289i
$832$	−105.421			−0.126708
$833$	−466.038	−	955.317i	−0.559469	−	1.14684i
$834$	−609.533			−0.730855
$835$		0			0
$836$	−55.7193	−	32.1696i	−0.0666499	−	0.0384803i
$837$	176.261	+	101.764i	0.210586	+	0.121582i
$838$	−356.184	−	616.928i	−0.425040	−	0.736191i
$839$			165.698i			0.197494i	0.995113	+	0.0987471i	$0.0314835\pi$
$839$			165.698i			0.197494i	−0.995113	+	0.0987471i	$0.968517\pi$
$840$		0			0
$841$	1745.57			2.07559
$842$	−961.701	+	555.238i	−1.14216	+	0.659428i
$843$	−462.929	+	801.816i	−0.549144	+	0.951146i
$844$	335.612	−	581.297i	0.397645	−	0.688741i
$845$		0			0
$846$			30.5414i			0.0361010i
$847$	−166.724	+	266.840i	−0.196841	+	0.315041i
$848$		−	88.4838i		−	0.104344i
$849$	−387.352	−	670.913i	−0.456245	−	0.790239i
$850$		0			0
$851$	−108.834	+	188.507i	−0.127890	+	0.221512i
$852$	115.514	+	200.076i	0.135580	+	0.234831i
$853$	1066.17			1.24991			0.624955	−	0.780661i	$-0.285117\pi$
$853$	1066.17			1.24991			0.624955	+	0.780661i	$0.285117\pi$
$854$	1290.38	+	45.0070i	1.51098	+	0.0527014i
$855$		0			0
$856$	186.098	+	322.331i	0.217404	+	0.376555i
$857$	111.325	−	192.821i	0.129901	−	0.224995i	−0.793737	−	0.608261i	$-0.791867\pi$
$857$	111.325	−	192.821i	0.129901	−	0.224995i	0.923638	+	0.383266i	$0.125201\pi$
$858$	−709.796	−	409.801i	−0.827269	−	0.477624i
$859$	−1313.46	+	758.329i	−1.52906	+	0.882805i	−0.529661	+	0.848209i	$0.677681\pi$
$859$	−1313.46	+	758.329i	−1.52906	+	0.882805i	−0.999401	+	0.0345956i	$0.988986\pi$
$860$		0			0
$861$	−15.5578	+	446.052i	−0.0180695	+	0.518063i
$862$			321.190i			0.372610i
$863$	119.543	−	69.0180i	0.138520	−	0.0799745i	−0.429139	−	0.903239i	$-0.641183\pi$
$863$	119.543	−	69.0180i	0.138520	−	0.0799745i	0.567658	+	0.823264i	$0.307849\pi$
$864$	150.688	+	86.9997i	0.174407	+	0.100694i
$865$		0			0
$866$	945.752	−	546.030i	1.09209	−	0.630520i
$867$	−314.476			−0.362717
$868$	−547.031	−	341.791i	−0.630221	−	0.393769i
$869$	252.732			0.290831
$870$		0			0
$871$	1874.36	+	1082.16i	2.15196	+	1.24243i
$872$	−98.3502	−	56.7825i	−0.112787	−	0.0651176i
$873$	−110.698	−	191.734i	−0.126802	−	0.219627i
$874$			32.4737i			0.0371552i
$875$		0			0
$876$	304.911			0.348072
$877$	534.875	−	308.810i	0.609892	−	0.352121i	−0.163031	−	0.986621i	$-0.552127\pi$
$877$	534.875	−	308.810i	0.609892	−	0.352121i	0.772923	+	0.634500i	$0.218794\pi$
$878$	−79.6818	+	138.013i	−0.0907538	+	0.157190i
$879$	436.650	−	756.300i	0.496757	−	0.860409i
$880$		0			0
$881$			425.629i			0.483120i	0.970386	+	0.241560i	$0.0776591\pi$
$881$			425.629i			0.483120i	−0.970386	+	0.241560i	$0.922341\pi$
$882$	−332.992	+	162.446i	−0.377542	+	0.184179i
$883$			295.270i			0.334394i	0.985923	+	0.167197i	$0.0534717\pi$
$883$			295.270i			0.334394i	−0.985923	+	0.167197i	$0.946528\pi$
$884$	−549.332	−	951.471i	−0.621416	−	1.07632i
$885$		0			0
$886$	−552.452	+	956.874i	−0.623535	+	1.07999i
$887$	844.884	+	1463.38i	0.952519	+	1.64981i	0.739947	+	0.672665i	$0.234850\pi$
$887$	844.884	+	1463.38i	0.952519	+	1.64981i	0.212571	+	0.977146i	$0.431816\pi$
$888$	381.037			0.429096
$889$	1184.13	−	629.676i	1.33198	−	0.708297i
$890$		0			0
$891$	39.2432	+	67.9713i	0.0440440	+	0.0762865i
$892$	−67.1628	+	116.329i	−0.0752946	+	0.130414i
$893$	10.9700	+	6.33354i	0.0122845	+	0.00709244i
$894$	54.2039	−	31.2946i	0.0606308	−	0.0350052i
$895$		0			0
$896$	721.895	+	451.048i	0.805686	+	0.503402i
$897$			153.197i			0.170788i
$898$	469.261	−	270.928i	0.522563	−	0.301702i
$899$	−1725.18	−	996.035i	−1.91900	−	1.10794i
$900$		0			0
$901$	83.6336	−	48.2859i	0.0928230	−	0.0535914i
$902$	−809.129			−0.897039
$903$	−7.45956	+	213.870i	−0.00826087	+	0.236844i
$904$	−383.409			−0.424124
$905$		0			0
$906$	−802.911	−	463.561i	−0.886215	−	0.511657i
$907$	382.848	+	221.038i	0.422104	+	0.243702i	0.695977	−	0.718064i	$-0.254972\pi$
$907$	382.848	+	221.038i	0.422104	+	0.243702i	−0.273873	+	0.961766i	$0.588305\pi$
$908$	214.854	+	372.138i	0.236623	+	0.409843i
$909$			320.861i			0.352982i
$910$		0			0
$911$	998.378			1.09591			0.547957	−	0.836507i	$-0.315406\pi$
$911$	998.378			1.09591			0.547957	+	0.836507i	$0.315406\pi$
$912$	93.4968	−	53.9804i	0.102518	−	0.0591890i
$913$	−92.0544	+	159.443i	−0.100826	+	0.174636i
$914$	−303.963	+	526.479i	−0.332563	+	0.576016i
$915$		0			0
$916$		−	39.4834i		−	0.0431041i
$917$	349.139	+	218.146i	0.380740	+	0.237891i
$918$			284.096i			0.309473i
$919$	154.797	+	268.116i	0.168441	+	0.291748i	0.937872	−	0.346982i	$-0.112794\pi$
$919$	154.797	+	268.116i	0.168441	+	0.291748i	−0.769431	+	0.638730i	$0.779460\pi$
$920$		0			0
$921$	345.364	−	598.188i	0.374988	−	0.649499i
$922$	−432.736	−	749.520i	−0.469344	−	0.812928i
$923$	1220.62			1.32245
$924$	−116.787	−	219.622i	−0.126393	−	0.237686i
$925$		0			0
$926$	−94.2280	−	163.208i	−0.101758	−	0.176250i
$927$	32.3088	−	55.9605i	0.0348531	−	0.0603674i
$928$	−1474.89	−	851.526i	−1.58932	−	0.917593i
$929$	443.269	−	255.921i	0.477146	−	0.275480i	−0.242080	−	0.970256i	$-0.577830\pi$
$929$	443.269	−	255.921i	0.477146	−	0.275480i	0.719226	+	0.694776i	$0.244496\pi$
$930$		0			0
$931$	−10.7064	+	153.293i	−0.0114999	+	0.164654i
$932$			626.737i			0.672464i
$933$	−358.682	+	207.085i	−0.384440	+	0.221956i
$934$	−777.476	−	448.876i	−0.832415	−	0.480595i
$935$		0			0
$936$	232.248	−	134.089i	0.248129	−	0.143257i
$937$	−592.935			−0.632801			−0.316401	−	0.948626i	$-0.602474\pi$
$937$	−592.935			−0.632801			−0.316401	+	0.948626i	$0.602474\pi$
$938$	832.762	+	1566.04i	0.887807	+	1.66955i
$939$	386.592			0.411706
$940$		0			0
$941$	−549.458	−	317.230i	−0.583909	−	0.337120i	0.178777	−	0.983890i	$-0.442786\pi$
$941$	−549.458	−	317.230i	−0.583909	−	0.337120i	−0.762685	+	0.646770i	$0.776119\pi$
$942$	−918.386	−	530.230i	−0.974932	−	0.562877i
$943$	75.6198	+	130.977i	0.0801907	+	0.138894i
$944$		−	1870.54i		−	1.98150i
$945$		0			0
$946$	−387.956			−0.410101
$947$	−571.239	+	329.805i	−0.603209	+	0.348263i	−0.770303	−	0.637678i	$-0.779895\pi$
$947$	−571.239	+	329.805i	−0.603209	+	0.348263i	0.167094	+	0.985941i	$0.446562\pi$
$948$	59.0444	−	102.268i	0.0622831	−	0.107878i
$949$	805.487	−	1395.14i	0.848775	−	1.47012i
$950$		0			0
$951$		−	495.391i		−	0.520916i
$952$	−21.9781	+	630.127i	−0.0230863	+	0.661898i
$953$		−	615.571i		−	0.645930i	−0.946411	−	0.322965i	$-0.895320\pi$
$953$		−	615.571i		−	0.645930i	0.946411	−	0.322965i	$-0.104680\pi$
$954$	−16.8309	−	29.1519i	−0.0176424	−	0.0305576i
$955$		0			0
$956$	46.6996	−	80.8861i	0.0488489	−	0.0846088i
$957$	−384.100	−	665.282i	−0.401359	−	0.695174i
$958$	942.013			0.983312
$959$	−40.4837	+	1160.69i	−0.0422145	+	1.21032i
$960$		0			0
$961$	286.605	+	496.415i	0.298237	+	0.516561i
$962$	−1437.41	+	2489.68i	−1.49419	+	2.58802i
$963$	232.883	+	134.455i	0.241831	+	0.139621i
$964$	169.830	−	98.0515i	0.176172	−	0.101713i
$965$		0			0
$966$	−66.5255	+	106.473i	−0.0688669	+	0.110220i
$967$		−	386.702i		−	0.399899i	−0.979806	−	0.199949i	$-0.935922\pi$
$967$		−	386.702i		−	0.399899i	0.979806	−	0.199949i	$-0.0640778\pi$
$968$	161.635	−	93.3202i	0.166979	−	0.0964052i
$969$	102.043	+	58.9145i	0.105307	+	0.0607993i
$970$		0			0
$971$	487.138	−	281.249i	0.501687	−	0.289649i	−0.227723	−	0.973726i	$-0.573128\pi$
$971$	487.138	−	281.249i	0.501687	−	0.289649i	0.729410	+	0.684077i	$0.239795\pi$
$972$	36.6727			0.0377291
$973$	−862.950	+	458.885i	−0.886896	+	0.471619i
$974$	−1959.79			−2.01211
$975$		0			0
$976$	−1259.68	−	727.279i	−1.29066	−	0.745163i
$977$	616.682	+	356.041i	0.631199	+	0.364423i	0.781216	−	0.624260i	$-0.214600\pi$
$977$	616.682	+	356.041i	0.631199	+	0.364423i	−0.150017	+	0.988683i	$0.547933\pi$
$978$	28.8878	+	50.0351i	0.0295376	+	0.0511607i
$979$			635.472i			0.649103i
$980$		0			0
$981$	−82.0504			−0.0836396
$982$	−1001.43	+	578.178i	−1.01979	+	0.588776i
$983$	−614.407	+	1064.18i	−0.625032	+	1.08259i	0.363502	+	0.931593i	$0.381581\pi$
$983$	−614.407	+	1064.18i	−0.625032	+	1.08259i	−0.988535	+	0.150995i	$0.951752\pi$
$984$	132.375	−	229.281i	0.134528	−	0.233009i
$985$		0			0
$986$		−	2780.64i		−	2.82012i
$987$	22.9930	+	43.2392i	0.0232959	+	0.0438087i
$988$			158.832i			0.160761i
$989$	36.2577	+	62.8001i	0.0366609	+	0.0634986i
$990$		0			0
$991$	621.249	−	1076.04i	0.626892	−	1.08581i	−0.361280	−	0.932457i	$-0.617660\pi$
$991$	621.249	−	1076.04i	0.626892	−	1.08581i	0.988172	−	0.153351i	$-0.0490064\pi$
$992$	655.811	+	1135.90i	0.661100	+	1.14506i
$993$	−933.617			−0.940199
$994$	848.337	+	530.050i	0.853457	+	0.533250i
$995$		0			0
$996$	43.0123	+	74.4995i	0.0431850	+	0.0747987i
$997$	−400.883	+	694.350i	−0.402089	+	0.696439i	−0.993978	−	0.109581i	$-0.965049\pi$
$997$	−400.883	+	694.350i	−0.402089	+	0.696439i	0.591889	+	0.806020i	$0.298382\pi$
$998$	−1387.23	−	800.920i	−1.39001	−	0.802525i
$999$	238.415	−	137.649i	0.238654	−	0.137787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.s.h.199.2		16
5.2	odd	4		105.3.n.a.31.1	✓	8
5.3	odd	4		525.3.o.l.451.4		8
5.4	even	2	inner	525.3.s.h.199.7		16
7.5	odd	6	inner	525.3.s.h.124.7		16
15.2	even	4		315.3.w.a.136.4		8
35.12	even	12		105.3.n.a.61.1	yes	8
35.17	even	12		735.3.h.a.391.7		8
35.19	odd	6	inner	525.3.s.h.124.2		16
35.32	odd	12		735.3.h.a.391.8		8
35.33	even	12		525.3.o.l.376.4		8
105.47	odd	12		315.3.w.a.271.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.1	✓	8	5.2	odd	4
105.3.n.a.61.1	yes	8	35.12	even	12
315.3.w.a.136.4		8	15.2	even	4
315.3.w.a.271.4		8	105.47	odd	12
525.3.o.l.376.4		8	35.33	even	12
525.3.o.l.451.4		8	5.3	odd	4
525.3.s.h.124.2		16	35.19	odd	6	inner
525.3.s.h.124.7		16	7.5	odd	6	inner
525.3.s.h.199.2		16	1.1	even	1	trivial
525.3.s.h.199.7		16	5.4	even	2	inner
735.3.h.a.391.7		8	35.17	even	12
735.3.h.a.391.8		8	35.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.18275 + 1.26021i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.17628 - 2.03737i) q^{4} +4.36551i q^{6} +(3.28656 + 6.18050i) q^{7} -4.15226i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-2.18275 + 1.26021i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.17628 - 2.03737i) q^{4} +4.36551i q^{6} +(3.28656 + 6.18050i) q^{7} -4.15226i q^{8} +(-1.50000 - 2.59808i) q^{9} +(4.36036 - 7.55236i) q^{11} +(-2.03737 - 3.52883i) q^{12} -21.5286 q^{13} +(-14.9625 - 9.34874i) q^{14} +(9.93785 + 17.2129i) q^{16} +(-10.8462 + 18.7862i) q^{17} +(6.54826 + 3.78064i) q^{18} +(2.71590 - 1.56803i) q^{19} +(12.1170 + 0.422628i) q^{21} +21.9799i q^{22} +(3.55799 - 2.05421i) q^{23} +(-6.22840 - 3.59597i) q^{24} +(46.9917 - 27.1307i) q^{26} -5.19615 q^{27} +(16.4579 + 0.574033i) q^{28} +50.8583 q^{29} +(-33.9213 - 19.5845i) q^{31} +(-28.9999 - 16.7431i) q^{32} +(-7.55236 - 13.0811i) q^{33} -54.6743i q^{34} -7.05767 q^{36} +(-45.8831 + 26.4906i) q^{37} +(-3.95209 + 6.84523i) q^{38} +(-18.6443 + 32.2929i) q^{39} +36.8122i q^{41} +(-26.9810 + 14.3475i) q^{42} +17.6504i q^{43} +(-10.2580 - 17.7674i) q^{44} +(-5.17748 + 8.96766i) q^{46} +(2.01959 + 3.49804i) q^{47} +34.4257 q^{48} +(-27.3971 + 40.6251i) q^{49} +(18.7862 + 32.5387i) q^{51} +(-25.3236 + 43.8618i) q^{52} +(-3.85542 - 2.22593i) q^{53} +(11.3419 - 6.54826i) q^{54} +(25.6631 - 13.6467i) q^{56} -5.43180i q^{57} +(-111.011 + 64.0923i) q^{58} +(-81.5032 - 47.0559i) q^{59} +(-63.3781 + 36.5913i) q^{61} +98.7226 q^{62} +(11.1276 - 17.8095i) q^{63} +4.89677 q^{64} +(32.9699 + 19.0352i) q^{66} +(-87.0635 - 50.2661i) q^{67} +(25.5164 + 44.1956i) q^{68} -7.11598i q^{69} -56.6975 q^{71} +(-10.7879 + 6.22840i) q^{72} +(-37.4147 + 64.8042i) q^{73} +(66.7676 - 115.645i) q^{74} -7.37773i q^{76} +(61.0079 + 2.12789i) q^{77} -93.9833i q^{78} +(14.4903 + 25.0980i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-46.3912 - 80.3519i) q^{82} -21.1116 q^{83} +(15.1140 - 24.1897i) q^{84} +(-22.2433 - 38.5266i) q^{86} +(44.0446 - 76.2875i) q^{87} +(-31.3594 - 18.1054i) q^{88} +(-63.1066 + 36.4346i) q^{89} +(-70.7551 - 133.057i) q^{91} -9.66528i q^{92} +(-58.7535 + 33.9213i) q^{93} +(-8.81655 - 5.09024i) q^{94} +(-50.2293 + 28.9999i) q^{96} +73.7985 q^{97} +(8.60469 - 123.201i) q^{98} -26.1622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 12 * q^4 - 24 * q^9	\( 16 q + 12 q^{4} - 24 q^{9} + 40 q^{11} + 32 q^{14} - 4 q^{16} + 96 q^{21} - 96 q^{24} + 240 q^{26} + 200 q^{29} - 252 q^{31} - 72 q^{36} + 24 q^{39} + 36 q^{44} - 164 q^{46} - 76 q^{49} + 36 q^{51} - 36 q^{54} + 392 q^{56} + 108 q^{59} - 792 q^{61} + 8 q^{64} + 48 q^{66} + 328 q^{71} + 280 q^{74} + 412 q^{79} - 72 q^{81} - 264 q^{84} + 356 q^{86} - 564 q^{89} - 228 q^{91} - 60 q^{94} - 216 q^{96} - 240 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 - 24 * q^9 + 40 * q^11 + 32 * q^14 - 4 * q^16 + 96 * q^21 - 96 * q^24 + 240 * q^26 + 200 * q^29 - 252 * q^31 - 72 * q^36 + 24 * q^39 + 36 * q^44 - 164 * q^46 - 76 * q^49 + 36 * q^51 - 36 * q^54 + 392 * q^56 + 108 * q^59 - 792 * q^61 + 8 * q^64 + 48 * q^66 + 328 * q^71 + 280 * q^74 + 412 * q^79 - 72 * q^81 - 264 * q^84 + 356 * q^86 - 564 * q^89 - 228 * q^91 - 60 * q^94 - 216 * q^96 - 240 * q^99

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